Contents ix
Part III
History and Philosophy
11 The Ultimate Replicating Machines . . . . . . . . . . . . . . . . 217
11.1 Mathematics: reproduction, transmission, error
correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
11.2 The Babel of mathematics . . . . . . . . . . . . . . . . . . . . . . 220
11.3 The nature and role of mathematical memes . . . . . 222
11.4 Mathematics and Origami . . . . . . . . . . . . . . . . . . . . . . 228
11.5 Copying by squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
11.6 Some stumbling blocks . . . . . . . . . . . . . . . . . . . . . . . . . 235
11.6.1 Natural language and music . . . . . . . . . . . . 235
11.6.2 Mathematics and the natural sciences. . . . 235
11.6.3 Genotype and phenotype . . . . . . . . . . . . . . . . 236
11.6.4 Algorithms of the brain . . . . . . . . . . . . . . . . . 236
11.6.5 Evolution of mathematics . . . . . . . . . . . . . . . 237
11.7 Mathematics as a proselytizing cult . . . . . . . . . . . . . 238
11.8 Fancy being Euclid? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
12 The Vivisection of the Cheshire Cat . . . . . . . . . . . . . . . 247
12.1 A few words on philosophy . . . . . . . . . . . . . . . . . . . . . . 247
12.2 The little green men from Mars . . . . . . . . . . . . . . . . . 251
12.3 Better Than Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
12.4 The vivisection of the Cheshire Cat . . . . . . . . . . . . . . 253
12.5 A million dollar question . . . . . . . . . . . . . . . . . . . . . . . 256
12.6 The boring, boring theory of snooks . . . . . . . . . . . . . . 260
12.6.1 Why are some mathematical objects more
important than others? . . . . . . . . . . . . . . . . . 260
12.6.2 Are there many finite snooks around? . . . . 262
12.6.3 Snooks, snowflakes, Kepler, and Palfy ´ . . . . 264
12.6.4 Hopf algebras . . . . . . . . . . . . . . . . . . . . . . . . . . 267
12.6.5 Back to ontological commitment . . . . . . . . . 270
12.7 Zilber’s Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
12.8 Explication of (in)explicitness . . . . . . . . . . . . . . . . . . . 273
12.9 Testing times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
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